I studied both forms of boxing for several years when I was a younger man. There is really not a way to answer your question as it was presented. There are too many variable to really compare one style to another. The skill of the fighter, and maybe a little luck, will almost always be the deciding factor in who wins a particular fight. The style of fighting is secondary to that. However, I'll lay out a couple of scenarios with different assumptions that might help you decide, based on your reason for asking the original question.

Scenario 1: Sport Fighting
-The two fighters are physically equal
-Both fighters are are adhering to the rules of their sport
-Both fighters are experienced and equally skilled in their respective discipline.

In this scenario I would expect the kick boxer have a slight advantage because he has twice as many options for striking at his disposal. Hands & feet vs just hands.

Scenario 2: Sport Fighting
-The two fighters are physically equal
-Both fighters are are adhering to the rules of their sport
-Both fighters are fairly new to their discipline...say less than 1 yr.

I would expect the traditional boxer to have the advantage in this fight, for exactly the opposite reason as in Scenario 1. The idea of practicing one punch a thousand time is better than a thousand punches one time. The traditional boxer will, in my experience gain skill more quickly, because he has only two weapons to master vs four.

Scenario 3: Combative Fighting
In a real life combative scenario assumptions will get you beat up or killed. Combative fights are not planned and end in under a minute, in most cases. If I were going to suggest to my brother one or the other of these arts for self defense, I would suggest traditional boxing. I have never been in a real fight where a kick was a huge benefit, but being able to use by hands effectively has saved me more than once.

Again, these answers are not meant to be idealistic or comprehensive, they are just based on my own experience.

Around 30 years ago I saw a 3 round exhibition bout in Miami Beach. Boxing champ Thomas Hearns took on Bill Wallace. It was a pretty good show and both guys displayed great skills. Wallace had the edge as long as his kicks came as a surprise to Tommy.

I think the great Joe Lewis once had a demo fight with Leon Spinks in the UK around the same time.